Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises - Page 59: 9

The x- and y-coordinates are the same for co-terminal angles. Since we use $x$ and $y$ to find $r$, then $x, y,$ and $r$ have the same values for co-terminal angles. Since the values of $x, y,$ and $r$ are used to find the values for the trigonometric functions, co-terminal angles have the same values for their trigonometric functions.

Co-terminal angles are located in the same position on the Cartesian plane. That is, co-terminal angles point in the same direction on the Cartesian plane. Therefore, the x- and y-coordinates are the same for co-terminal angles. Since we use $x$ and $y$ to find $r$, then $x, y,$ and $r$ have the same values for co-terminal angles. Since the values of $x, y,$ and $r$ are used to find the values for the trigonometric functions, co-terminal angles have the same values for their trigonometric functions.